MATLAB#limitations

MATLAB was invented by mathematician and computer programmer Cleve Moler.{{cite journal | last1=Chonacky | first1=N. | last2=Winch | first2=D. | title=Reviews of Maple, Mathematica, and Matlab: Coming Soon to a Publication Near You | journal=Computing in Science & Engineering | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=7 | issue=2 | year=2005 | issn=1521-9615 | doi=10.1109/mcse.2005.39 | pages=9–10| bibcode=2005CSE.....7b...9C | s2cid=29660034 }} The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and started developing MATLAB for his students as a hobby. He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe. This was followed by Fortran code for linear equations in 1971.

Before version 1.0, MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics. And no ODEs or FFTs."{{Cite web|title=A Brief History of MATLAB|url=https://www.mathworks.com/company/newsletters/articles/a-brief-history-of-matlab.html|access-date=2021-09-04|website=www.mathworks.com|language=en}}

The first early version of MATLAB was completed in the late 1970s. The software was disclosed to the public for the first time in February 1979 at the Naval Postgraduate School in California.{{cite journal|url=http://www.tomandmaria.com/Tom/Writing/MolerBio.pdf|first=Thomas|last=Haigh|title=Cleve Moler: Mathematical Software Pioneer and Creator of Matlab|publisher=IEEE Computer Society|journal=IEEE Annals of the History of Computing}} Early versions of MATLAB were simple matrix calculators with 71 pre-built functions.{{cite journal | last1=Moler | first1=Cleve | last2=Little | first2=Jack | title=A history of MATLAB | journal=Proceedings of the ACM on Programming Languages | publisher=Association for Computing Machinery (ACM) | volume=4 | issue=HOPL | date=June 12, 2020 | pages=1–67 | issn=2475-1421 | doi=10.1145/3386331| doi-access=free }} At the time, MATLAB was distributed for free{{cite book | last1=Xue | first1=D. | last2=Press | first2=T.U. | title=MATLAB Programming: Mathematical Problem Solutions | publisher=De Gruyter | series=De Gruyter STEM | year=2020 | isbn=978-3-11-066370-9 | url=https://books.google.com/books?id=0Y7ZDwAAQBAJ&pg=PP21 | access-date=September 16, 2020 | page=21}}{{cite book | last=Press | first=CRC | title=Solving Applied Mathematical Problems with MATLAB | publisher=CRC Press | year=2008 | isbn=978-1-4200-8251-7 | url=https://books.google.com/books?id=V4vulPEc29kC&pg=PA6 | access-date=September 16, 2020 | page=6}} to universities.{{cite book | last1=Woodford | first1=C. | last2=Phillips | first2=C. | title=Numerical Methods with Worked Examples: Matlab Edition | publisher=Springer Netherlands | series=SpringerLink : Bücher | year=2011 | isbn=978-94-007-1366-6 | url=https://books.google.com/books?id=L90JVxIvA0YC&pg=PA1 | access-date=September 16, 2020 | page=1}} Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.{{cite book | last=Tranquillo | first=J.V. | title=MATLAB for Engineering and the Life Sciences | publisher=Morgan & Claypool Publishers | series=Synthesis digital library of engineering and computer science | year=2011 | isbn=978-1-60845-710-6 | url=https://books.google.com/books?id=ofWpMryW0lgC | access-date=September 17, 2020 | page=}}{{RP|5}}

In the 1980s, Cleve Moler met John N. Little. They decided to reprogram MATLAB in C and market it for the IBM desktops that were replacing mainframe computers at the time. John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.

MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in Las Vegas. MathWorks, Inc. was founded to develop the software and the MATLAB programming language was released. The first MATLAB sale was the following year, when Nick Trefethen from the Massachusetts Institute of Technology bought ten copies.{{cite web | last=LoTurco | first=Lori | title=Accelerating the pace of engineering | website=MIT News |publisher=Massachusetts Institute of Technology | date=January 28, 2020 | url=https://news.mit.edu/2020/accelerating-pace-engineering-mathworks-fellows-0128 | access-date=September 16, 2020}}

By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use. The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks. Many of the toolboxes were developed as a result of Stanford students that used MATLAB in academia, then brought the software with them to the private sector.

Over time, MATLAB was re-written for early operating systems created by Digital Equipment Corporation, VAX, Sun Microsystems, and for Unix PCs. Version 3 was released in 1987.{{cite journal | last1=Gatto | first1=Marino | last2=Rizzoli | first2=Andrea | title=Review of MATLAB, Version 4.0 | journal=Natural Resource Modeling | publisher=Wiley | volume=7 | issue=1 | year=1993 | issn=0890-8575 | doi=10.1111/j.1939-7445.1993.tb00141.x | pages=85–88| bibcode=1993NRM.....7...85G }} The first MATLAB compiler was developed by Stephen C. Johnson in the 1990s.

In 2000, MathWorks added a Fortran-based library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C. MATLAB's Parallel Computing Toolbox was released at the 2004 Supercomputing Conference and support for graphics processing units (GPUs) was added to it in 2010.

Some especially large changes to the software were made with version 8 in 2012.{{cite book | last1=Cho | first1=M.J. | last2=Martinez | first2=W.L. | title=Statistics in MATLAB: A Primer | publisher=CRC Press | series=Chapman & Hall/CRC Computer Science & Data Analysis | year=2014 | isbn=978-1-4665-9657-3 | url=https://books.google.com/books?id=X0IqBgAAQBAJ | access-date=September 17, 2020 | page=}} The user interface was reworked{{fact|date=February 2021}} and Simulink's functionality was expanded.{{cite book | last1=Xue | first1=D. | last2=Chen | first2=Y. | title=System Simulation Techniques with MATLAB and Simulink | publisher=Wiley | series=No Longer used | year=2013 | isbn=978-1-118-69437-4 | url=https://books.google.com/books?id=6d7iAAAAQBAJ&pg=PT17 | access-date=October 15, 2020 | page=17}}

By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.

For a complete list of changes of both MATLAB an official toolboxes, check MATLAB previous releases.{{cite web|title=MATLAB Previous releases|url=https://www.mathworks.com/support/requirements/previous-releases.html|publisher=MathWorks|accessdate=Dec 3, 2024}}

The MATLAB application is built around the MATLAB programming language.

Common usage of the MATLAB application involves using the "Command Window" as an interactive mathematical shell or executing text files containing MATLAB code.{{cite web|url=http://www.mathworks.com/help/matlab/index.html|title=MATLAB Documentation |publisher=MathWorks|access-date=August 14, 2013}}

An example of a "Hello, world!" program exists in MATLAB.

disp('Hello, world!')

It displays like so:

Hello, world!

Variables are defined using the assignment operator, =.

MATLAB is a weakly typed programming language because types are implicitly converted.{{cite web|title=Comparing MATLAB with Other OO Languages|url=http://www.mathworks.com/help/matlab/matlab_oop/matlab-vs-other-oo-languages.html|work=MATLAB|publisher=MathWorks|access-date=August 14, 2013}} It is an inferred typed language because variables can be assigned without declaring their type, except if they are to be treated as symbolic objects,{{cite web|title=Create Symbolic Variables and Expressions|url=http://www.mathworks.com/help/symbolic/creating-symbolic-variables-and-expressions.html|work=Symbolic Math Toolbox|publisher=MathWorks|access-date=August 14, 2013}} and that their type can change.

Values can come from constants, from computation involving values of other variables, or from the output of a function.

For example:

>> x = 17

x =

17

>> x = 'hat'

x =

hat

>> x = [3*4, pi/2]

x =

12.0000 1.5708

>> y = 3*sin(x)

y =

-1.6097 3.0000

A simple array is defined using the colon syntax: initial:increment:terminator. For instance:

>> array = 1:2:9

array =

1 3 5 7 9

defines a variable named array (or assigns a new value to an existing variable with the name array) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the initial value), increments with each step from the previous value by 2 (the increment value), and stops once it reaches (or is about to exceed) 9 (the terminator value).

The increment value can actually be left out of this syntax (along with one of the colons), to use a default value of 1.

>> ari = 1:5

ari =

1 2 3 4 5

assigns to the variable named ari an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the increment.

Indexing is one-based,{{cite web|title=Matrix Indexing|url=http://www.mathworks.com/help/matlab/math/matrix-indexing.html|publisher=MathWorks|access-date=August 14, 2013}} which is the usual convention for matrices in mathematics, unlike zero-based indexing commonly used in other programming languages such as C, C++, and Java.

Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to separate the rows. The list of elements should be surrounded by square brackets []. Parentheses () are used to access elements and subarrays (they are also used to denote a function argument list).

>> A = [16, 3, 2, 13 ; 5, 10, 11, 8 ; 9, 6, 7, 12 ; 4, 15, 14, 1]

A =

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

>> A(2,3)

ans =

11

Sets of indices can be specified by expressions such as 2:4, which evaluates to [2, 3, 4]. For example, a submatrix taken from rows 2 through 4 and columns 3 through 4 can be written as:

>> A(2:4,3:4)

ans =

11 8

7 12

14 1

A square identity matrix of size n can be generated using the function eye, and matrices of any size with zeros or ones can be generated with the functions zeros and ones, respectively.

>> eye(3,3)

ans =

1 0 0

0 1 0

0 0 1

>> zeros(2,3)

ans =

0 0 0

0 0 0

>> ones(2,3)

ans =

1 1 1

1 1 1

Transposing a vector or a matrix is done either by the function transpose or by adding dot-prime after the matrix (without the dot, prime will perform conjugate transpose for complex arrays):

>> A = [1 ; 2], B = A.', C = transpose(A)

A =

1

2

B =

1 2

C =

1 2

>> D = [0, 3 ; 1, 5], D.'

D =

0 3

1 5

ans =

0 1

3 5

Most functions accept arrays as input and operate element-wise on each element. For example, mod(2*J,n) will multiply every element in J by 2, and then reduce each element modulo n. MATLAB does include standard for and while loops, but (as in other similar applications such as APL and R), using the vectorized notation is encouraged and is often faster to execute. The following code, excerpted from the function magic.m, creates a magic square M for odd values of n (MATLAB function meshgrid is used here to generate square matrices {{mvar|I}} and {{mvar|J}} containing {{tmath|1:n}}):

[J,I] = meshgrid(1:n);

A = mod(I + J - (n + 3) / 2, n);

B = mod(I + 2 * J - 2, n);

M = n * A + B + 1;

MATLAB supports structure data types.{{cite web|title=Structures|url=http://www.mathworks.com/help/matlab/structures.html|publisher=MathWorks|access-date=August 14, 2013}} Since all variables in MATLAB are arrays, a more adequate name is "structure array", where each element of the array has the same field names. In addition, MATLAB supports dynamic field names{{cite web|title=Generate Field Names from Variables|url=http://www.mathworks.com/help/matlab/matlab_prog/generate-field-names-from-variables.html|publisher=MathWorks|access-date=August 14, 2013}} (field look-ups by name, field manipulations, etc.).

When creating a MATLAB function, the name of the file should match the name of the first function in the file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores. Variables and functions are case sensitive.{{cite web|title=Case and Space Sensitivity|url=https://www.mathworks.com/help/matlab/matlab_prog/case-and-space-sensitivity.html|publisher=MathWorks|access-date=November 1, 2019}}

{{sxhl|2=matlab|1=

rgbImage = imread('ecg.png');

grayImage = rgb2gray(rgbImage); % for non-indexed images

level = graythresh(grayImage); % threshold for converting image to binary,

binaryImage = im2bw(grayImage, level);

% Extract the individual red, green, and blue color channels.

redChannel = rgbImage(:, :, 1);

greenChannel = rgbImage(:, :, 2);

blueChannel = rgbImage(:, :, 3);

% Make the black parts pure red.

redChannel(~binaryImage) = 255;

greenChannel(~binaryImage) = 0;

blueChannel(~binaryImage) = 0;

% Now recombine to form the output image.

rgbImageOut = cat(3, redChannel, greenChannel, blueChannel);

imshow(rgbImageOut);

}}

MATLAB supports elements of lambda calculus by introducing function handles,{{cite web|title=Function Handles|url=http://www.mathworks.com/help/matlab/function-handles.html|publisher=MathWorks|access-date=August 14, 2013}} or function references, which are implemented either in .m files or anonymous{{cite web|title=Anonymous Functions|url=http://www.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html|publisher=MathWorks|access-date=August 14, 2013}}/nested functions.{{cite web|title=Nested Functions|url=http://www.mathworks.com/help/matlab/matlab_prog/nested-functions.html|publisher=MathWorks.}}

MATLAB supports object-oriented programming including classes, inheritance, virtual dispatch, packages, pass-by-value semantics, and pass-by-reference semantics.{{cite web|url=http://www.mathworks.com/help/matlab/object-oriented-programming.html |title=Object-Oriented Programming|publisher=MathWorks|access-date=August 14, 2013}} However, the syntax and calling conventions are significantly different from other languages. MATLAB has value classes and reference classes, depending on whether the class has handle as a super-class (for reference classes) or not (for value classes).{{cite web|title=Comparing Handle and Value Classes|url=http://www.mathworks.com/help/matlab/matlab_oop/comparing-handle-and-value-classes.html|publisher=MathWorks}}

Method call behavior is different between value and reference classes. For example, a call to a method:

object.method();

can alter any member of object only if object is an instance of a reference class, otherwise value class methods must return a new instance if it needs to modify the object.

An example of a simple class is provided below:

classdef Hello

methods

function greet(obj)

disp('Hello!')

end

end

end

When put into a file named hello.m, this can be executed with the following commands:

>> x = Hello();

>> x.greet();

Hello!

{

"version": 2,

"width": 400,

"height": 200,

"data": [

{

"name": "table",

"values": [

{

"x": 3,

"y": 1

},

{

"x": 1,

"y": 3

},

{

"x": 2,

"y": 2

},

{

"x": 3,

"y": 4

}

]

}

],

"scales": [

{

"name": "x",

"type": "ordinal",

"range": "width",

"zero": false,

"domain": {

"data": "table",

"field": "x"

}

},

{

"name": "y",

"type": "linear",

"range": "height",

"nice": true,

"domain": {

"data": "table",

"field": "y"

}

}

],

"axes": [

{

"type": "x",

"scale": "x"

},

{

"type": "y",

"scale": "y"

}

],

"marks": [

{

"type": "rect",

"from": {

"data": "table"

},

"properties": {

"enter": {

"x": {

"scale": "x",

"field": "x"

},

"y": {

"scale": "y",

"field": "y"

},

"y2": {

"scale": "y",

"value": 0

},

"fill": {

"value": "steelblue"

},

"width": {

"scale": "x",

"band": "true",

"offset": -1

}

}

}

}

]

}

MATLAB has tightly integrated graph-plotting features. For example, the function plot can be used to produce a graph from two vectors x and y. The code:

x = 0:pi/100:2*pi;

y = sin(x);

plot(x,y)

produces the following figure of the sine function:

350px

MATLAB supports three-dimensional graphics as well:

MATLAB supports developing graphical user interface (GUI) applications.{{cite web| url=http://www.mathworks.com/discovery/matlab-gui.html | title=MATLAB GUI | publisher=MathWorks | date=April 30, 2011 | access-date=August 14, 2013}} UIs can be generated either programmatically or using visual design environments such as GUIDE and App Designer.{{cite web|title=Create a Simple GUIDE GUI|url=http://www.mathworks.com/help/matlab/creating_guis/about-the-simple-guide-gui-example.html|publisher=MathWorks|access-date=August 14, 2014}}{{cite web|title=MATLAB App Designer|url=https://www.mathworks.com/products/matlab/app-designer.html|publisher=MathWorks|access-date=November 1, 2019}}

MATLAB can call functions and subroutines written in the programming languages C or Fortran.{{cite web|title=Application Programming Interfaces to MATLAB|url=http://www.mathworks.com/help/matlab/programming-interfaces-for-c-c-fortran-com.html|publisher=MathWorks|access-date=August 14, 2013|archive-date=September 15, 2017|archive-url=https://web.archive.org/web/20170915020649/http://www.mathworks.com/help/matlab/programming-interfaces-for-c-c-fortran-com.html|url-status=dead}} A wrapper function is created allowing MATLAB data types to be passed and returned. MEX files (MATLAB executables) are the dynamically loadable object files created by compiling such functions.{{cite web|title=Create MEX-Files|url=http://www.mathworks.com/help/matlab/create-mex-files.html|publisher=MathWorks|access-date=August 14, 2013|archive-date=March 3, 2014|archive-url=https://web.archive.org/web/20140303193228/http://www.mathworks.com/help/matlab/create-mex-files.html|url-status=dead}}{{cite web|title=Connecting C and Matlab | last=Spielman | first=Dan | publisher=Yale University, Computer Science Department | date=February 10, 2004 | url=http://www.cs.yale.edu/homes/spielman/ECC/cMatlab.html | access-date=May 20, 2008}} Since 2014 increasing two-way interfacing with Python was being added.{{cite web|title=MATLAB Engine for Python|url=http://www.mathworks.com/help/matlab/matlab-engine-for-python.html|publisher=MathWorks|access-date=June 13, 2015}}{{cite web|title=Call Python Libraries|url=http://www.mathworks.com/help/matlab/call-python-libraries.html|publisher=MathWorks|access-date=June 13, 2015}}

Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB,{{cite web|title=External Programming Language Interfaces|url=http://www.mathworks.com/help/matlab/external-interfaces.html|publisher=MathWorks|access-date=August 14, 2013|archive-date=March 11, 2014|archive-url=https://web.archive.org/web/20140311003229/http://www.mathworks.com/help/matlab/external-interfaces.html|url-status=dead}}{{cite web|title=Call Perl script using appropriate operating system executable|url=http://www.mathworks.com/help/matlab/ref/perl.html|publisher=MathWorks|access-date=November 7, 2013}} and many MATLAB libraries (for example XML or SQL support) are implemented as wrappers around Java or ActiveX libraries. Calling MATLAB from Java is more complicated, but can be done with a MATLAB toolbox{{cite web|url=http://www.mathworks.com/products/javabuilder/ |title=MATLAB Builder JA |publisher=MathWorks |access-date=June 7, 2010}} which is sold separately by MathWorks, or using an undocumented mechanism called JMI (Java-to-MATLAB Interface),{{cite web |url=http://undocumentedmatlab.com/blog/jmi-java-to-matlab-interface/ |first=Yair |last=Altman |title=Java-to-Matlab Interface |publisher=Undocumented Matlab |date=April 14, 2010 |access-date=June 7, 2010 |archive-date=September 5, 2015 |archive-url=https://web.archive.org/web/20150905153327/http://undocumentedmatlab.com/blog/jmi-java-to-matlab-interface |url-status=dead }}{{cite web|title=matlabcontrol JMI|url=https://code.google.com/p/matlabcontrol/wiki/JMI|first=Joshua |last=Kaplan}} (which should not be confused with the unrelated Java Metadata Interface that is also called JMI). Official MATLAB API for Java was added in 2016.{{cite web|title=MATLAB Engine API for Java|url=http://www.mathworks.com/help/matlab/matlab-engine-api-for-java.html|publisher=MathWorks|access-date=September 15, 2016}}

As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.{{cite web|title=MaMa: Calling MATLAB from Mathematica with MathLink|url=http://library.wolfram.com/infocenter/MathSource/618/|publisher=Wolfram Library Archive|first=Roger |last=Germundsson |work=Wolfram Research |date=September 30, 1998}}{{cite web|title=MATLink: Communicate with MATLAB from Mathematica|url=http://matlink.org/|access-date=August 14, 2013|author1=rsmenon |author2=szhorvat|year=2013}}

Libraries also exist to import and export MathML.{{cite web |first=Michael |last=Weitzel |url=http://www.mathworks.com/matlabcentral/fileexchange/7709-mathml-importexport |title=MathML import/export |publisher=MathWorks - File Exchange |date=September 1, 2006 |access-date=August 14, 2013 |archive-date=February 25, 2011 |archive-url=https://web.archive.org/web/20110225010921/http://www.mathworks.com/matlabcentral/fileexchange/7709-mathml-importexport |url-status=dead }}

In 2020, MATLAB withdrew services from two Chinese universities as a result of US sanctions. The universities said this will be responded to by increased use of open-source alternatives and by developing domestic alternatives.{{Cite web|date=2020-06-12|title=US military ban locks two Chinese universities out of popular software|url=https://www.scmp.com/news/china/diplomacy/article/3088854/us-military-ban-locks-two-chinese-universities-out-popular|access-date=2020-11-06|website=South China Morning Post|language=en}}

• Comparison of numerical-analysis software
• List of numerical-analysis software

{{Reflist|30em}}

{{Refbegin}}

• {{cite book |last=Gilat |first=Amos |title=MATLAB: An Introduction with Applications 2nd Edition |year=2004 |publisher=John Wiley & Sons |isbn= 978-0-471-69420-5 |ref=none}}
• {{cite book |author-link1= Alfio Quarteroni |last1=Quarteroni |first1=Alfio |first2=Fausto |last2=Saleri |title=Scientific Computing with MATLAB and Octave |year=2006 |publisher=Springer |isbn= 978-3-540-32612-0 |ref=none}}
• {{cite book |last=Ferreira |first=A.J.M. |title=MATLAB Codes for Finite Element Analysis |year=2009 |publisher=Springer |isbn= 978-1-4020-9199-5 |ref=none}}
• {{cite book |last=Lynch |first=Stephen |title=Dynamical Systems with Applications using MATLAB |year=2004 |publisher=Birkhäuser |isbn=978-0-8176-4321-8 |ref=none}}

{{Refend}}

{{Sister project links

|wikt=no |n=no |q=no |s=no

|commons=Category:MATLAB

|b=MATLAB Programming

|v=MATLAB essential

}}

• {{Official website|https://www.mathworks.com/products/matlab.html}}

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{{Image Processing Software}}

{{Linear algebra}}

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